sum variable obs Mean Std. Dev. Min XEN wage 191 4.770733 5. 823419 1.02 17.72 looks 191 2. 157068 - 6620859 1 a. Construct the 95% confidence interval of the population mean of wage. b. Interpret the 95% confidence interval that you constructed in question 2. Would a 99% confidence interval be wider or narrower than the 95% confidence interval constructed in question a? c. The claim is made that the population mean wage is $ 4. Formulate the null hypothesis and alternative hypothesis. Use the confidence interval you obtained in part a to decide whether you would like to support this claim or not. The significance level is 0.05. Then the researcher focuses on the subsample of women with above average look (i.e. looks=3). The following Stata command summarizes the variable wage for those women with above average look (i.e. looks=3). Read the output table and answer question 6-9. sum wage if looks==] Variable obs Mean Etd. Dev . Min Max wage 59 5 . 655085 9.735509 1.28 77 .72 d. The claim is made that the population mean wage of people with above average look is $ 9. Formulate the null hypothesis and alternative hypothesis. Calculate the t-statistic. Use the critical value approach to test at the significance level 0.01. Clearly state the details along the way and remember to interpret your results. For question 5, use the following facts. invttail(191,0.005)=2.6018; invttail(191,0.01)=2.3460; invttail(191,0.025)=2.0679; invttail(191,0.025)=1.9725; invttail(191,0.05)=1.6529; invttail(191,0.1)=1.2860 invttail(191,0.005)=2.6020; invttail(190,0.01)=2.3461; invttail(190,0.025)=2.0679; invttail(191,0.025)=1.9725; invttail(190,0.05)=1.6529; invttail(190,0.1)=1.2860